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Pitol1 1 1 JH Oelian churuty W 1 1 1 921 shuxoul 0t 1...

Question

Pitol1 1 1 JH Oelian churuty W 1 1 1 921 shuxoul 0t 1

pitol 1 1 1 JH Oelian churuty W 1 1 1 921 shux oul 0t 1



Answers

$\left[ \begin{array}{lll}{1} & {1} & {1} \\ {1} & {2} & {3} \\ {0} & {1} & {1}\end{array}\right]$

This video's gonna go through the answer to question number 11 from chapter 9.3. So ask to use real reduction to find the inverse off the matrix. That 11 one 121 Thio three. So So we conform the combination matrix with the identity and they tried refugees. Okay, so if we subtract to you off the top equation from the bomb equation, then we're gonna get zero one that to you, minus 20 Maybe it's gonna be minus 201 on the inside. And if we should bottle subtract one of the first question from the middle equation, that's gonna be zero That's gonna be one on that's going to zero months. Well, on zero on me, the top equation as it is, Savior zero. Okay, so now we get to be a stick in court because on left inside the bomb equation on the middle or after the bottom row of the majors in the middle of the matrix. All the same, which means that the ah, the row is off the matrix linearly dependence, which by their a born in the book, means that er the identity that's all right with me

Well, everyone, this is Ricky and they were working on a problem. Five from a model test number six. And so this is a question asking us about sphere that's inscribed in a cube. And what the ratio of the falling sphere to the booth. All right, So to start this question, let's write down the formulas for both of our severe and for acute first fear, 4/3 choir cute. And for the volume of the Cube, a heart issues this will rather Cuba's the length aside. Yes, threes as cute. And then, if we translate this where the length of side ISS equal to the radius spear, get or rather the diameter of the spear, get what you are. That's a cute Wallace to paint way Now if we look at the ratio votes spear. Q. Start with Why are huge? Huge. You see that? Ready? I drop out. And for my what a fine two. Everything's fine Pi over 63.14 over six, which is about 0.52 I hope this video is helpful. Seeing that

Okay for this one. We have a is equal to 12 negative. One 011 and zero. Negative 11 So the characteristic equation for this problem is given by negative Lambda Cubed plus three Lambda squared minus four. Lambda plus two is equal to zero. And when we solve this equation, it's a cubic equation. So you will get the three argon values as 11 plus I and one minus. I noticed that these talking visor complex congregants. So now if we have the Lambda equals one, then upon solving the system, eh? Minus I times u equals zero. We will get that use equal t times 100 and for Lambda equals one. Plus I, using a similar process, we end up getting that you sequel to a T times I'm minus two negative I and one no, for Lambda Contra Kit equals one minus I, which is given here. Then that implies that you is equal to it. Turns out that the Egan vectors are also conflicts congregates of each other. So you was simply gonna be equal to a T times negative. I'm minus two guy and one

We have this flow chart and we have to find the output of this flow chart. So let's start executing this flow chart before we execute each operations. When we want let's try to understand what exactly this flow chart does. It starts with the start command, then we have some operation box. We're in the values of A. And the ceo initialized and then some genius to diseases squired and then added with A. And is in fact doubled over here. And then it checks whether the value of a is still less than eight and when it does it will go ahead and or do these operations once again. So basically we have a loop over here It gets repeated as long as the value of a. is less than eight. once the value of is not less than eight. That is If a is either eight or anything more than eight like 9 then the local stop and it will start printing the value of C. So let's start executing this one x 1. So initially the value of the equal to one & C Equal to two. And when it comes over here the sea is getting updated by squiring the value of C. And then added with eight. So when we square the value of C we get to square is four. And when you add with a that is one we get sequel to fight. So therefore the current value is equal to five. And the next statement we have A is doubled. So equal to a start to, this is basically is getting double Which means this is the initial value of eight and double it will get to. So therefore these are the two values which we have done now. That is equal to five and equal to two. Well then how this decision box which checks whether it is still less than eight, Which is in fact true, that is two is less than eight. Yes. So that means the control will be shifted back to this point which means we are into the next to loop. So in the next two loop, let's write down the current values of AIDS and sees. So is already updated too two and she is now updated to fight. So these are the values that we are going to it place when we place this look. So then once again she's getting updated by squiring the sea and adding with a which means the sea will be square. That is five x squared. So therefore if you do that it will be 25 Plus getting added with a. That is too. So this gives value. See the new value of sequel to 27 And once again is getting doubled. So this is the value of a. That is too when a double two will get a call to four and once again we check whether still If a is to less than eight so is less than eight. Yes this is is therefore the control will be shifted back to the this point which means we are into the next loop. So let's write on the existing values of A. Or the updated values of A. And C. You know that this is the an updated value of we put here And c. is 27 so we put the C over kid And then once again the sea is getting squired and added with a. Which means c equal to 27 Times 27-plus 4. So when it's choir 27 This is equal to 729 plus food Which is equal to 7:33. Therefore the updated value of c equal to 733 and still and then the next statement we held this getting doubled as usual which means this four is getting doubled so therefore equal to eight now. And we have this decision is eight less than eight. No it is not. So therefore the loop will stop over here. It will come out of the loop and it will execute the next statement which means it prints the value of sleep. You know that the greater values equal to 77 33. So therefore at this point the computer will print the value 733 which means this option is correct


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